When logging in with kdm I only get the desktop background colour and the mouse pointer. No menu, no toolbar and no shortcuts working to try to launch any application. I had to type '"restart kdm" and use another windowmanager.

Doesn't icewm-session start the task bar? The bar should show up anyway, but icewm-session might be a work-around. Another work-around might be adding the lines,
ShowTaskBar = 1
TaskBarAutoHide = 0
TaskBarShowStartMenu = 1
to ~/.icewm/preferences or ~/.icewm/prefoverrides
These are all default, but setting them might work.
I've had no trouble with the taskbar (same icewm on Lucid, current on Lucid, ? on Jaunty), it might not be the package.